A Forchheimer’s Law-Based Well Hydraulics Model Considering Pore Void Clogging for Groundwater Injection

This study developed a generalized non-Darcian radial flow model incorporating pore clogging effects to analyze its impact on high-velocity flow around a recharge well.The non-Darcian flow was described using the Forchheimer equation,with time-dependent intrinsic hydraulic conductivity (K_D(t)) and inertial hydraulic conductivity (K_N(t)) introduced to characterize clogging evolution.A quasi-steady-state approximate semi-analytical solution was derived using linearization and Laplace transform,and a numerical solution was developed using the segmented nonlinear Galerkin method.Results show that:in constant-rate injection tests (CRTs),decreased K_D(t) and K_N(t) or increased clogging zone radius (r_c) elevates the hydraulic head (s) in the clogged zone but has negligible impact on the unclogged region.When r_c exceeds the non-Darcian flow zone,reduced K_N(t) expands the non-Darcian flow region.In constant-head injection tests (CHTs),decreased K_D(t) and K_N(t) or increased r_c reduce s throughout the aquifer,with K_D(t) reduction limiting the influence of non-Darcian flow on s.The permeability reduction due to clogging causes an inflection point at r=r_c on the s-logr curve in both CRTs and CHTs and a “rise-then-fall” pattern on the s-logt curve in CHTs.These characteristics are more pronounced under dominant non-Darcian flow.The findings provide a theoretical basis for dynamic assessment and prediction of aquifer clogging.